Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28% below the target pressure. Suppose the target tire pressure of a certain car is 30 psi (pounds per square inch.)
(a) At what psi will the TPMS trigger a warning for this car?
(b) Suppose the tire pressure is a normally distributed random variable with a standard deviation equal to 2psi. If the car's average tire pressure is on target, what is the probability that the TPMS will trigger a warning?

Step-by-step explanation:

a)The pressure level that will trigger a warning is

30 - 30*0.28 = 21.6 psi

b) The probability that the TPMS will trigger warning at 21.6 psi, given that tire pressure has a normal distribution with average of 30 psi and standard deviation of 2 psi is:

where x = 21.6, μ = 30 and σ = 2

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it